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# Math: Basic Tutorials : Solving Percent Change Problems

## Solving Percent Change Problems

A percent change problem asks how much a quantity has increased or decreased compared to its original value, e.g. the population of a city increases from last year to this year. This section shows you how to calculate percent increase or decrease.

## Example

### Examples

## Summary and Worksheet

## Attribution

Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on the titles below to view each example.

The price of admission into a museum increased from 26 dollars to 36 dollars per person. Find the percent increase. Round your final answer to the nearest tenth of a percent.

Line 1: What are you being asked to find? We are being asked to find the percent increase.

Line 2: Choose a variable to represent it. Let p be the percent increase.

Line 3: Find the amount of the increase by subtracting the original amount from the new amount, so the increase is 36 minus 26 equals 10.

Line 4: Find the percent increase. 10 is what percent of 26?

Line 5: Translate into algebra so the equation is 10 equals p times 26.

Line 6: Divide both sides of the equation by 26 to solve for p, so the equation is 10 divided by 26 equals 26p divided by 26.

Line 7: Simplify and round to the nearest thousandth so 0 decimal 3 8 5 equals p.

Line 8: Convert to a percent by multiplying by 100 percent so 38 decimal 5 percent equals p.

Line 9: Write a statement that answers the question. Therefore, the new admission price represents a 38 decimal 5 percent increase over the old admission price

The population of a city was 672 000 in 2010. The population of the city in 2020 is 630 000. Find the percent decrease. Round your final answer to the nearest tenth of a percent.

Line 1: What are you being asked to find? We are being asked to find the percent decrease.

Line 2: Choose a variable to represent it. Let p be the percent decrease.

Line 3: Find the amount of the decrease by subtracting the new population from the original population, so the decrease is 672 000 minus 630 000 equals 42 000.

Line 4: Find the percent decrease. 42 000 is what percent of 672 000?

Line 5: Translate into algebra so the equation is 42 000 equals p times 672 000.

Line 6: Divide both sides of the equation by 672 000 to solve for p, so the equation is 42 000 divided by 672 000 equals 672 000p divided by 672 000.

Line 7: Simplify and round to the nearest thousandth so 0 decimal 0 6 3 equals p.

Line 8: Convert to a percent by multiplying by 100 percent so 6 decimal 3 percent equals p.

Line 9: Write a statement that answers the question. Therefore, the population decreased by 6.3 percent.

- Summary: Solving Percent Change Problems - PDF - Opens in a new windowThis document contains a short (1 – 2 page) summary of this topic as well as detailed examples to illustrate key concepts. Use this summary to review this topic.
- Worksheet: Percent Change Problems - PDF - Opens in a new windowThis document contains practice questions on this topic. Use the worksheet to test your knowledge and practice the skills learned in this module. The answers to the practice questions are provided at the end.